We will eventually consider the case when (U) fails and perform blow-up sequence for reductive and unipotent stabilisers. For the unipotent stabilisers we will use §REF  based on [1]}. As observed in §REF , as well as [2]} and [3]}, we can obtain an explicit description of the open set we get a quotient of, provided the minimal weight space is not entirely blown up at any stage of the process. To ensure this, we introduce the following weaker assumption than (U).
